FIG. 1 represents a simplified target tracking system 10. System 10 tracks a target, illustrated as being an aircraft 12, by the use of multiple radar systems 14, 16. Radar system 14 includes a radar antenna 14a, which transmits and receives radar signals illustrated by “lightning bolt” symbols 18. Portions of the transmitted signals 18 are reflected by target 12 and return to the radar antenna 14a. The returned signals allow the generation of measurements at an output port 14o of radar system 14. Radar system 16 includes a radar antenna 16a, which transmits and receives radar signals illustrated by “lightning bolt” symbols 20. Portions of the transmitted signals 20 are reflected by target 12 and return to the radar antenna 16a. The returned signals allow the generation of measurements at an output port 16o of radar system 16. These measurements include values of at least target position, possibly in the form of range and angles from the radar systems 14 and 16. A possible scenario is that radar systems 14 and 16 have measurements which are corrupted by unknown random measurement noises, characterized by a covariance and unknown time-varying biases with known bounds. The biases may be, for example, the result of sensor misalignment. Furthermore, radar system 16 provides data with time latency, but which are more accurate (less measurement noise) than those provided by radar system 14. The measurements are applied to a processing arrangement 22, which determines from the measurements various target parameters, which may include course (direction of motion), speed, and target type. The estimated position of the target, and possibly other information, is provided to a utilization apparatus or user, illustrated in this case as being a radar display 24. The operator (or possibly automated decision-making equipment) can make decisions as to actions to be taken in response to the displayed information. It should be understood that the radar tracking system 10 of FIG. 1 is only one embodiment of a general class of estimation systems for systems with distributed sensors such as nuclear, chemical, or manufacturing factories or facilities, control processes subject to external parameter changes, space station subject to vibrations, automobile subject to weather conditions, and the like.
State-of-the-art tracking systems utilize measurements fed with time delays from multiple sensors to a processing site. These sensors may have different measuring accuracies (i.e., random errors) and unknown measurement biases that may be time-varying within physical bounds. Furthermore, these sensors may be geographically dispersed over a region of interest. Availability of reliable high bandwidth communication media allows such a topology of distributed multiple sensors for real-time processing of the measurements. Therefore, latent measurements from a remote sensor could arrive after state estimation at the current time is complete.
In spite of today's high bandwidth and fast switching communication network, physical distances, path diversity and relays may result in different delays from various sensors to the processing site. Let a sensor S1 measure a tracked object at time t1 and a sensor S2 measure that same object at time t2 where t2>t1. It is possible that the measurement from sensor S1 may arrive many sampling intervals after the measurement from sensor S2 has already been processed. A simple decision methodology is to throw out the late-arriving measurement from sensor S1, and not process it at all. However, if sensor S1 is the more accurate sensor, this methodology does not make good use of the available sensor resources.
A difficulty is that accounting for measurements received out of sequence, as frequently happens in situations of multiple sensor tracking with variable communication delays between sensors, greatly complicates the design of a Kalman filter, particularly when more than one subsequent measurement is processed before an out-of-sequence measurement is received. A solution to this problem is discussed in a pending patent application entitled “REDUCED STATE ESTIMATION WITH MULTISENSOR FUSION AND OUT-OF-SEQUENCE MEASUREMENTS”, filed on Mar. 30, 2005, in the names of P. Mookerjee and F. Reifler.
Consider the problem of tracking an airplane whose trajectory in three dimensions is an arbitrary curve with bounded instantaneous turn rate and tangential acceleration. The parameters of this tracking problem are the turn rate ω (which can be related to the curvature of the trajectory) and the tangential acceleration α. Sensors, such as multiple radars, observe the position of this airplane. Each sensor is subject to alignment errors which cause it to be rotated by an unknown amount from its nominal alignment, possibly as a consequence of imperfect mechanical mounting, flexure of the array structure due to temperature effects etc. These small or infinitesimal rotations constitute a vector b. The parameters, ω, α, and b are neither exclusively constant nor strictly white noise stochastic processes, but vary arbitrarily in time within physical bounds.
This problem belongs to a more general problem of estimating the state of a system using biased measurements. A solution to this problem is discussed in a pending patent application entitled “REDUCED STATE ESTIMATION WITH BIASED MEASUREMENTS”, filed on Apr. 22, 2005, in the names of P. Mookerjee and F. Reifler.
The method of the prior art is to estimate the states of a system when measurements are either out-of-sequence or biased. Improved or alternative estimators are desired for coping with biased measurements which are also delayed.